Wednesday, September 28, 2011

Modeling Unit 5

Unit V: Constant Force Particle Model

"Atwood Machine" with vernier track
From there, we started the next unit.  Here's what each end of the track looked like (the middle is just a track)

Jon changed the first question slightly:
What factors will effect the motion? (between letting go of the cart and hanging mass hitting ground)
What factor effects the cart’s acceleration?
Hanging mass
Mass of car
Friction: {adjust tilt of track until cart rolls at constant speed}
(pasco hanger approx. applies force to balance friction)
Mass of pulley
Mass of the earth/gravity
Angle of the track - ?
Starting speed -?

{Chris showed us a quicker way of working through the process by guiding us to eliminate the factors mentioned that cannot be adjusted (Mass of Earth) or that could be removed with creative lab design.  The last two options we left open, that depending on your class, you may or may not want to divide and conquer.}

Purpose: What is the graphical & mathematical relationship that exist between the mass of the cart and the force that is accelerating it.

Before getting started, we talked about multiple variations to this experiment
• Keeping the mass of the hanger while adding mass to the car
• Using photogate(s) above the track instead of motion detector
• Variation of this option is to attach picket fence to cart the cart and use vernier program
• Using kinematic equations and measure total time with stopwatch for total distance measured
• Having the students predict the mass of the system from data, and then, after showing prediction to the teacher, measuring the mass and comparing results to predictions {I like this!}

Equipment
Attach right angle to cart
Pulley at end of track
Hanger
String
Motion detector
Standard masses

Next up were some demonstrations of  Newton's 3rd Law:

Same track set up, with Force sensors attached to the top of each car.  The twist for this demonstration is to use the magnets to apply to force between the two cars and not the direct contact.  There are a couple of things to note for this demonstration.  Have one car against the stopper and start with the second car "far away" from the first car.  Zero both probes, and make sure you reverse the direction for one of them so they both have positive in the same direction of the track.  Have the magnets inside the car so the same pole faces outward and thus repel the cars.  Push the force probe of the second car (not the car itself)

From there, were picked up on the lab with which we finished yesterday.  Before starting the experiment we briefly discussed the merit of breaking the lab groups into different types of investigations, in which we would have 3 different trials: "A" would look at keeping the mass of the cart constant, but adding mass to the hanger; "B" would keep the hanger constant, and add mass to the car; "C" would move mass from the car to the hanger, keeping the mass of the system constant.  In an effort to save time, we have everyone do option "C" but I may or may not look at all the groups (maybe in my honors class?)

Also showing a way to move through the whiteboard process more quickly (as needed by time constraints or if class is not productive in meetings), Jon walked us through a "Circle the wagons" meeting.  In this format, all the groups show their white boards, and the teacher leads the group to try to draw conclusions in looking at all the results at once.

{As we were getting started, Jon also mentioned that when you are "normal" whiteboard meeting after a lab, in subsequent labs, start with a different group each time and change the order you call the groups forward.}

During the meeting, we had a great discussion on whether you should explain/guide to the students before starting the lab that they will need to plot Force vs acceleration so that the slope is mass, or wait until the end.
{My thought is to wait until the end, have all the groups manipulate their graphs, as teacher does it on projected screen}

At this point, Jon showed us a quick follow up demo/lab (used vernier "Lab 9 – Newton’s 2nd Law")
Jon taped an accelerometer to the force probe (Jon uses Velcro tape at his school).  Then you just click the record data button, and then push the cart back and forth.  Viola, data showing $F \propto a$

From there, we started individual work on Unit V worksheet 1 (#'s 1-4) and worksheet 2 (#'s 1-3)

As we got started, we briefly discussed strategies for word problems (w/ forces).  A summary of what we said was:
• Have students sketch what is happening and identify the system with dotted circle/box
• Get the words out of the word problem
• Create a Free Body Diagram
• Next to FBD, draw an arrow showing the direction of acceleration
• That will be "+" direction for the problem
• This convention will aid circular motion problems later in the year

Notes from whiteboard session:
•  Wkst 2: #2 is a great problem since a given number isn’t use in the calculation, but rather for analysis at the end.
• Wkst 2: #3 mass not given, so students need to determine it from the Weight
• Chris- Make sure units are included in the calculation not just at the end
• Possibly change wording of problem since the normal force changes not F­­­w
Jon then went on to describe how he helps his students understand "elevator" problems.  If you are standing on a bathroom scale, and you want to increase your "weight" you can pull on the bottom of the counter and squeeze the scale.  This is the same effect as when the elevator is accelerating upwards.  On the contrary, if you want to lose "weight," you can push on the top of the counter and push you body off the scale.  This same effect occurs when the elevator accelerates downward.

From there, we Jon showed us some fun demos
1. Have student kneel w/elbows touching knees & hands “praying”.  Put chapstick at tip if fingers.  Then have student place hands behind his/her back. They then need to try to knock over the chapstick by touching their nose to it.  Due to differences in center of mass, girls should be able to do this, while boys usually can't.
2. Have student stand facing the wall, with toes touching the base of the wall.  Have student take 3 steps (toe to back of heel) away from the wall.  Bend at the waist $90^o$ with their forehead touching the wall.  Place a small chair (or other "small" mass) in their hands and tell them to stand up.  Again, boys will struggle,  girls will tend to be successful.
3. Have one student (biggest student) sit all the way back into a chair with his/her feet flat on the floor.  Have a second  student (smallest) stand in front of first student and push into the first student's forehead.  Tell first student, without moving their feet, to stand up.  At the same time, the second student pushes on the forehead of the first, preventing him/her from standing up.
4. Have student stand with right shoulder and outside of right foot touching the wall.  Then tell the student to lift his/her left foot.
Friction Lab
We then moved on to a lab on Friction. We used a friction block and force probe.  The basic procedure was to the block at constant speed with different masses resting on top of the block.  We used the vernier file "Lab 12a Static Kinetic Fric."  A sketch of the graph produced looked basically like this:

The max force represents the static friction force, and when the force is basically horizontal (red line) then the friction force equals the measured force.

To speed things up, each group given different normal force ("zero mass" was mass of block plus 250 g) and needed to get good data (slope of oscillating data was as close to horizontal as possible).  Find the average value of the force using the statistics button.

Unit V Feedback
The Good:
• We felt we were becoming comfortable using computer based equipment
• Continuation of the sequence of showing 3rd law  (adding non-contact interaction)
• Low tech demo’s/labs

• Modified atwood machine has a lot of physics baggage we’ll need to use as a paradigm

Suggestions:
• When it comes to multiple representations of event
• FBD, motion maps, graphs, equations
• Only let students say verbal description of the event– Carbon dioxide not "See" "Oh" "Two"

Modeling Unit 4

Unit IV: Free Particle Model

Jon began the unit by asking us to describe the motion of the following event:
{He tweeked the activity as we do not have student desks, what he said to do in the classroom was to have a student sit at a desk that everyone can see.  Push the desk so that it starts moving at near constant speed, and then stop pushing.}

We were to describe the motion using our 4 tools (written description, motion maps, kinematic equations, and kinematic graphs (x vs t, v vs t, and a vs t).  {We were to make those tools describe the motion from before it started moving until after it stopped.}

After we were done with our individual answers, Chris shortened the process by just asking individuals to share their ideas/draw their graphs on the board.  {I'm guessing that he was trying to make up for lost time due to our lengthy discussion earlier, and would do this through whiteboards, but I could be wrong.}

During this process, students often want to jump to why the objects are doing what they are doing.  Which leads to a discussion on forces.

From there, Chris said that he then does a mini-lecture on contact forces (forces caused by to objects being in contact) and fundamental forces (Gravity, Electro-magnetic, Strong, and Weak). {He said that he doesn't get into Normal and Friction forces at this point, but I might.  I'll have to think on this some more.}

From there, he makes use of a hovertoy (examples here and here, or make your own similar by hot-gluing the top to a "sport-top" water bottle to a CD, and slipping an inflated balloon over the cap. If your school has an airtrack, that would obviously work as well. ).  With the air turned off, push the puck across the table.  Then turn on the air, and push the puck.  Ask the students what is different about the two trials.  Guide the discussion until they realize that, for the whole series of demos, no force acting on the object leads to no change in motion; force applied leads to a change in motion. "No Force, No Change."

{Newton's first law, but like much of modeling, focus on the concept not the name.  Chris mentioned that he steers the conversation away from the term inertia, and instead focuses on the terms "balanced" and "unbalanced" forces.}

From there, Chris introduced Free Body Diagrams (FBD), in which you show the forces acting on the object (or system).  He started with a FBD for the puck resting on the table:

The circle/dot in the center represents the object, the arrows represent the forces acting on the object.  Chris said it was up to you if you wanted a convention such as all arrows point away from dot, or arrows point to show how the force is acting (Push-inwards arrow, Pull-outwards arrow).  The convention used in modeling for the name of the force is the numerator is the acting object, the denominator is the object in question.  So the two forces here are the force of the table on the puck $F_{T/P}$ and the force of Earth on the puck $F_{E/P}$ (AKA the force of gravity/ weight of the puck).  If need be, remind students that the earth is the object that creates gravity, not that gravity is an object itself (Thus $F_{G/P}$ would be incorrect).

{By the way, when I was a wise-a, acted like a student, and said that the puck is resting on the table, so the table can't be pushing up, Jon went into the closet, found a bowling ball and rolled it to me.  He told me to lift the ball and hold it shoulder-high at arms length.  Then asked if I'm pushing the ball to keep it at that same height. Touche Jon!}
{By the way, a bowling ball is another cheap prop you can use for the earlier part of the lab.}

He then showed a FBD for the puck at the instant he first pushed it:

The added force is the force of "your" hand on the puck $F_{H/P}$

From this discussion, Chris had us work on Worksheet 1, and then had groups whiteboard answers. {My only concern with this is that many of these problems get into 2D FBD's.  I'm not sure if I want to get to that before I've really had the students do any hands-on with forces}

Chris mentioned that this worksheet does a great job of bringing out student misconceptions about forces.  Most students get stuck, so instead of whiteboarding answers, for this problem, he has them whiteboard their questions about the worksheet.

At this point, we moved on to the paradigm demonstration: Dropping a bowling ball from shoulder height.
We again went through the usual questions, however, Chris added one more to the mix:
What do you notice? What can you measure? What forces are present? What can you manipulate?
We then created the purpose: To determine the graphical and mathematical relationship between the force of the earth on the object and mass.

We were then thrown a curveball for the experiment, we were given a Vernier Dual Range Force Sensor (Jon mentioned that spring scales work just fine) and some standard masses, and guided to plot mass vs Force.  As we saw that the data made a straight line, we could find the slope of that line.

Each group then whiteboarded their results.  About the time the groups were getting lazy with the presentation (since we all had approximately the same numerical results), Chris threw out a question, "What is the connection between the slope of your line and dropped bowling ball from the start of the lab?"

For the groups that plotted Force in units "N" (which are, as of this point in the process, possibly unknown units) vs mass in kg, we found that the slope was eerily similar to the number we measured when finding the acceleration of object dropped (picket fence and rubber ball over motion detector) in the previous units.  That acceleration describes the acceleration of the dropped ball.  If all the groups used grams (which are the units printed on most standard masses), guide them through questioning to the value of slope with mass in units of kilograms.

Chris also noted, that making the connection between $N/kg$ and $m/s^2$ will payoff when Electric fields come up later in the year. {Obviously, this point will need to be reinforced throughout this unit and others for the students to remember it during E&M.}

We began today with a series of demonstrations that together, will help students to conceptualize the "Normal" Force.  First up was a very nifty contraption which shows that even small forces do in fact, move a wall (Jon said that this even works with a brick wall!)

Jon attached a metal rod to the wall with modeling clay.  Between the table an the rod, he placed a T-pin his Biology teachers unknowningly provided to him.  Glued to the T-pin is a small piece of mirror.  A few feet away, they had a laser set up, which was pointed at the mirror.  As you push on the wall, the wall moves, which causes the bar to roll the mirror, which in turn changes the reflection of the laser.  Students can see the effect of you pushing on the wall by watching the laser dot on the opposite wall move up and down. {Hopefully that made sense.}  Here's a picture of the setup:

Next he suggested (they didn't find any springs until later in the day) to take the bowling ball and set it on top of a spring, which is itself on the table (you'll bring that part up later).  Ask the students what the spring is doing to the ball (to which they should reply pushing it up)

Then, set the ball on top of soft foam, and again ask what the foam is doing.  Then set it on some firm foam.  Next, set it on top of 2 meter sticks (elevated at each end by some blocks) so that the students can see the meter sticks flex in the middle.  Finally, place the ball on top of table by itself.  In each case, ask what the "base" is doing to the bowling ball.  If they still don't get it, ask what the table was doing to the spring at the beginning of the sequence.

At this point, ask the student to draw a FBD of the ball resting on the table.  At this point, now call the upward force of the table on the ball, the Normal force.  Ask what would happen to this force if the table surface was rotated (incline plane), and lead students to the fact that it is always perpendicular to the surface.

Jon then went on to describe how he uses surgical tubing ("borrowed" from the chem teacher) and student sitting/standing on a homemade hovercraft (here are the directions to make it*)(You can use on office chair if you don’t have hovercraft).  Here's a picture of the setup with an office chair {I guess Jon didn't want to bring his hovercraft from Minnesota, how rude}

*Modifications Jon made to the procedure:
Blue tarp works fine, don’t need that pattern of holes – he just put 30 small triangular holes throughout
Duct tape around between small disc and big disc
Use the biggest fender washer @home depot you can find instead of the coffee lid
Make the hole (at the very end) as close to the size of shopvac nozzle as you can (need a tight seal)

Take the class into the hallway, and ask for 2 volunteers.  One sits/stands on chair/hovercraft and holds a meterstick at his/her waist.  The second you tell to pull the rubber tubing to a fixed distance.  You tell the person to pull the other victim volunteer such that the distance the tubing is stretched does not change.  Let the carnage begin.  If you want to maintain some sense of safety have the other students line the hallway to help keep the demonstration moving down the hall instead of into doorways and other obstacles.

You can take the sequence to the next level by now asking what would happen if the person seated in the chair/standing on hovercraft were to throw a medicine ball?  (Demonstrate if you have one).  Now ask what would happen if you had a magic contraption that dropped unlimited medicine balls so you could constantly throw them?  Tell them, let's not imagine it. let's do it.  Grab a $CO_2$ fire extinguisher and release the trigger while sitting/standing.  (Jon said he removes any hose/nozzle, and that he worked out a deal with a local supply company to get an old extinguisher, and get ~$10 refills. He said one full extinguisher will work for all his classes.) At this point bring the class back inside and have them summarize what all has happened, using FBDs as needed. Guide the students to the idea of Newton's 3rd Law: If "A" exerts a force on "B" to the "right," then "B" exerts a force on "A" to the "left." From there, we moved on to individually, complete Unit IV wkst 3 (Jon told us that he doesn't use this sheet as written, but modifies it for his 1st yt students) {Has students do the FBD’s but modifies to do progressions in steps, not all at once} {chris inserts a week or two of material from the math modeling curriculum to review trig concepts.} {does math review before this unit not at beginning of the year like most teachers} After completing the worksheet, we whiteboarded our results. Notes from WB: #4 – group made error on purpose – switching sine & cosine (Acting as students saying that cos is always the horizontal component of a vector) Jon's series of questions: Which leg of the triangle is the longer leg, so which one should be bigger? • What on the diagram will be equal to the Vertical leg? (Answer: weight) • What will be equal to the Horizontal leg? (Answer: T1) • Based on triangle, which should be the bigger force? (Since vert. leg>horizontal leg, Weight) • Does you answer match that fact? #8 – Jon – Giancoli has a great problem w/ lawn mower {Which in looking through my copy looks like #26 in chapter 4} One question they asked the group (mainly to have some fun at their expense) If floor is frictionless, how does he push the broom? At that point someone mentioned this Cartoon over at xkcd http://xkcd.com/669/ Next we Whiteboarded sections of Hake “Socratic Pedagogy in the intro phys lab Due to time constraints, Jon showed us a trick if we ever need to move things along: If running short on time – have all students display boards, then ask if anyone has questions. Address the questions as needed, and move on. Here a link to SDI labs as provided by Chris From there we moved on to another Demo to continue to explain Newtons$3^{rd}$Law: Equipment: 2 spring scales & 2 volunteers Scales attached between the 2 people, 1 person pulls while the other just holds on, then they switch, lastly both pull on the scales. (If you don't have large spring scales, use 2 bathroom scales/ or vernier force plates) For bathroom scales (have a "reader" looks over each shoulder & call out values) Next they set up 2 vernier carts each w/ force sensor attached, on cart track track (Jon mentioned that Steiner (sp?) has variations of worksheets in the modeling website, probably under password wall for those that attended the workshop) (Before you begin, zero the sensors and make sure one has direction flipped, or you won't see both sets of data in the plot) 1st Trial- both cars moving with equal mass & approx same speed 2nd Trial - add standard masses to one car, so the collision has uneven mass 3rd Trial - One stationary vs one moving 4th Trial - One moving fast, the other slow 5th Trial - Cars start together and explosion with cart “spring” {Obviously (?) you could keep going if you feel the need Next, they took the sensors off the cars, and attached them at the hooks, and plotted real-time data of the students pulling the sensors apart. Unit IV: Worksheet 4 (Due to the complexity, Jon has his students first just answer the A/B/C part of the problems and has students whiteboard their answers. Then he has them draw the FBDs, however, they only need to depict the interactions of block A on B and B on A (no other forces yet), and again, they quickly whiteboard their answers. He then walks them through one or two of the problems, and assigns the rest for homework. Whiteboard results at the start of the next class) We again finished the unit we feedback. Chris said they were going to limit the discussion to 15 minutes. What we liked: Wkst 3 – we liked FBD & crunching numbers (we're physics teachers, what do you expect) Wkst 4 – we also liked how this helped to solidify Newt’s 3rd law We liked the progression of demos for 3rd law Especially the Laser reflection based on pushing the wall For the most part, talking about Forces with little math (have yet to bring up$a=\frac{F}{m}$) What we didn't like: Would like for this unit to have more lab and less time on complicated worksheets (Demos are good, but students are watching not doing) {someone mentioned possibly using force table labs to introduce 2D/trig} We felt that Worksheet 1 would be too big of a jump our students and would have like to see what Chris did to get his kids ready for it. A few had concerns that their students would never be able to ever do some of this work Chris also said that for his AP class he has a summer assignment, which is primarily a math review Modeling Unit 3 Unit III: Uniform Acceleration Particle Model We began the "Cart on an Incline Plane Lab." After talking to Jon and Chris about Brian Frank's Blog during our lunch break, Jon and Chris altered the first question to begin the cycle by asking "What do you see/notice?" Again, we moved through "What can you measure?" and "What can you manipulate?" before arriving at the purpose: "to determine the mathematical and graphical relationships between position and time for a cart on an incline plane at a fixed angle. As a group, we seemed to struggle with this process this time. I'm not sure if we are taking our role in "student mode" too seriously and confusing ourselves in the process. We didn't seem satisfied to look at this relationship and many wanted to add more quantities such as mass and angle into the procedure. One good suggestion was to focus the students back on the first question, "What do you see?" By using what is already on the board, we can steer the students to the necessary target of this unit. I might add that we should include some help to our students to focus on the actual demonstration we are doing (cart rolling down a fixed ramp) and try to dissuade them from altering the set up. Possibly reminding them that our job is to create the experience that will teach them the necessary component of physics, and we chose this exact one for a reason. After we were settle on the debate, Jon told us to use the motion detector to acquire "clean data" for the cart. When asked what he meant, he said, "You'll see what I mean." He put on the board for us to then manually calculate 10 values of "average speed" over the range of our data (he originally put instantaneous, but later corrected it). He also remembered later that he usually has the file "01a Graph matching.cmbl" from the physics file loaded onto the computers, so that the velocity will not be automatically calculated for the students. For the average velocity, he tells the students to use the position and clock readings from just before and after the point we are using to calculate the average velocity. Jon also mentioned that during the acquisition of data, and the subsequent creation of the whiteboards, he would talk to the groups about the significance of the data produced (if you started the cart after the motion detector, what do the initial data points mean? points after the cart hit the bottom of the track?). We next analyzed the graphs we made from the cart on an incline plane lab to derive the kinematic equations. Although this only takes about 10-15 minutes, it made this post too long. So I made a separate post to show the process. Although most texts give these equations, many omit the entire process. For the sake of helping your students foster their connection between the graphs and the equations, Jon recommends spending the time to show these derivations. {My guess is that you could either do this during whiteboarding, or as a mini-lecture (for those that aren't quite ready to give up the reins, and want to be a sage on the stage again).} After showing all the derivations, we moved on to Lab Extension: Speeding Up and Slowing Down. {As I've noted at least once before, we were given version 3 of this worksheet. However, I'm only seeing version 2 on the modeling website. I guess that's one more reason you need to go to the workshop and not just read my blog.} Jon told us that he gives the students all the equipment except for the motion detector. Jon said that after the individual groups show him the completed worksheet, he provides the motion detector. After the students have all completed acquiring the data/graphs, he has them white board what they got for a given problem. Chris does it a little differently. He never gives them the detector, but rather has the students make the predictions for HW, and then the groups whiteboard their predictions at the beginning of class. He then projects the actual results after the class has come to agreement for the each given problem. {My$0.02 on this is that I like Chris's approach better (sorry Jon).}

By the way, I had never seen motion maps that showed both velocity and acceleration at the same time.  For those like me, you plot the velocity above the displacement vector and acceleration below.  Have the points that represent the same time line up vertically.  I've tried to show what the map for #1 would look like below:

The blue vectors represent the velocity and the red vectors represent the acceleration for an object accelerating from rest.
{I'm honestly not sure how to draw the first point for the acceleration portion, whether they should be inline with the arrow overlapping the second point, or as shown with the first point slightly above the second.  I'm guessing how I have it is correct.  And no, I didn't waste the time to make sure the arrows were to scale.  Remember motion maps are qualitative, not quantitative.}

A couple points made by Jon and Chris:

#3 is the first instance for the students where an object is speeding up even though it has a negative acceleration.  You need to socratically question the students (What is happening to the magnitude of the velocity?   What then is the sign of the acceleration?  Can a negative acceleration increase the velocity?).  According to both Chris and Jon, this is a confusing idea, since they are used to describing a negative acceleration as a deceleration (a term you should dissuade the students from using).

#4 is a similarly confusing example in that the acceleration is positive but the object is slowing down.  Again, use Socratic questioning to lead the students to this idea.

#6 Jon omits this problem as changing the origin doesn't really come up later in the curriculum.  He said that it's up to you and your students.  Do you want/have time to spend on this?
{My thoughts are that I might leave this out for standard level, buy include it for the honors level of my classes.  If I have more than 6 lab groups in honors (which I did this past year ('10-'11)), I might make additional problems with the adjusted origin so each group whiteboards their own problem.}

From there we worked on Worksheet 2Worksheet 2a, and a supplementary worksheet.

2a: #3 Jon mentioned that students tend to struggle with all the technical vocabulary in this problem.

2a:#5 Chris asked the group presenting: “I remember a problem from the earlier work, where the negative velocity and it was speeding up.  Why is this different?” {Your trying to get the kids to focus on the speeding up when acceleration is in the same direction as motion, (and slowing down when opposite) not based on +/- sign}

Wkst III:
1 c&d Jon mention that these problems are very tricky for students.

We next moved on to another experiment using a Vernier Photogate and the Vernier Picket Fence. (note: you may need some of the accessories to attach the photogate to a ringstand).  We used the "picket fence" file provided by vernier.

We were asked to get one measurement of "g" for the picketfence by itself, and one value while a hanging weight was attached to the picketfence.  Jon and Chris made this a competition among groups to see who could get the closest value to the accepted (9.80665 $m/s^2$) for each set of measurements.
{I'm not sure if I would tell my students the correct value or not.  I would probably just calculate the class average and then ask the students to explain our error.  One side note, one of my pet peeves is "human error."  To me that is a student being lazy and not wanting to think about what they did wrong.  I would push my students to say that the picket fence was rotated one way or another, photogate wasn't level, etc.}

From there, we then did another "competition" lab where we were provided the motion detectors, a rubber ball (similar to traditional dodgeball that could actually leave a mark, not the foam ones given now.)  {Don't get me started on that one.}, and a metal filing shelf (similar to this, only it was one level not two). The shelf was used over the top of the detector to help protect it from the ball.  The basic procedure was to toss the ball above the motion detector and have it fall towards the detector.  Again, the group with the closest value to "g" received a prize.  We used the "ball toss" file provided by vernier.
{I think I might introduce video analysis at this point, either have the students do it in their groups, or run this as a demo, videotaping the students tossing the ball.  Then I would show on the smartboard how to use video analysis.  I would probably use the tool in LoggerPro, however, seeing Rhett Allain use VideoTracker throughout his blog, makes me think it might be worth it to have the students download and use that programHowever it might be worth leaving video analysis until we get to 2D motion.}

We ended the day by whiteboarding sections of the assigned reading from the previous night.  Instead of giving a summary of the summary, I would just say we read Aron's book and discussed 2.7 - 2.16 (excluding 2.14).  It builds off most of the concepts already discussed yesterday.  For those that haven't read it, it's a great text that explains many of the students' misconceptions and strategies to help overcome them.

We started today by finishing our whiteboard summaries of Ch 2 from Aron's book.  Since I didn't go into detail on the Day 5 post, I'll omit them here as well.

From there, we wrapped up Unit III with some feedback to Jon and Chris:

What worked:
• The worksheet "stacks of kinematic graphs" - we felt that it was a great tool for helping students convert from one type of kinematic graph to another.  Chris mentioned that if/when you have students whiteboard this, to make sure that they display the graphs vertically.
• Worksheet: Speeding up/slowing down - we liked that this allowed us/students to predict what they thought would occur, then later them seeing the results.
• We liked that there were multiple labs that were short, as you could get more hands on time, but not use multiple days to do different activities.
• We liked seeing the graphical proof of kinematic equations
• We liked the reading from Aron's book, especially the misconceptions he mentioned, and tools to help overcome them.
What didn’t work:
• We said that we would like more insight into the "mechanic" of implementation the modeling cycle
• What does the day to day flow look like
• When do learning objectives come into play (some are at schools that must display the objectives for that day's lesson at the start of class)
• Pacing of course
• Some of us that aren't familiar with the content want more time to complete activities, and we also recognize that we need tools to overcome what we see in the workshop; some people are done with nothing to do, while others are struggling to keep up.
• Some asked, "What to do if we don’t have loggerpro/equipment?"
• One other thing we liked in the first cycle that didn't occur here was the division of Labor/variation of control variables.  {I'm not sure how you would fit that in, but that's what came up in discussion}
{To those in the workshop (merely reading) that want to see the pacing of a class, one website I found was Mark Schober's Website.  Another great blog that you might find useful is Action-Reaction, one especially nice feature is that he organized his blogroll for different subjects (I'll try to get to that at some point).}
Miscellaneous Questions:
• How often do the students need to do formal lab reports, and how do those "Work?"
• As already mentioned, what are some ideas for extensions of labs for “faster” students
For the first question, Jon referred us to some of the resources at the beginning of the modeling binder (here, here, and here).
For the second question, Jon mentioned that he often splits up the groups that are done and have them help the groups that are going slower.

One other point that came up, was that if you need help keeping everyone engaged, assign each person in the group a roll. {When I need to do this, I use "Leader," "Secretary," "Technician," and "Gofor."  The leader in is charge of making sure the group is on task.  The Secretary is in charge of recording all necessary information/procedures/equipment/etc.. The technician is in charge of running the actual experiment.   The gofor (some call it the Yeoman) is the person in charge of "going for" stuff.  He/she gets the equipment at the beginning, is in charge of cleaning up at the end, and the assistant for all other jobs.}

One other conversation that came up was to make sure that everyone in the group knew one anothers' names.  Jon mentioned that he was surprised how many problems could be avoided if they knew that one simple fact.  He makes it a point to quiz students each others' names at beginning of new lab groups.

When Chris got a chance to address the question about objectives, he said he often uses some of the resources from the modeling curriculum to make review's

Kelly O'Shea has a blog that I love, which focuses a great deal on Standards Based Grading.  (One oversimplification of SBG is you report grades based on learning objectives of the unit. ) (Here are her objectives for Honors Physics, by the way).  When I asked her when she reveals her objectives to her students, she said:
Usually try to hand them out at the start of the unit. I would say few students look at them before they are preparing for an assessment. Some probably don’t look at them until they get the test back and look at their scores.
Jon mentioned that he often uses the provided Unit Objectives sheet to create a review.  Chris said that he often has the 3 ring-binder out when groups are whiteboarding, and often asks questions right out of the teacher notes (post lab discussions especially)

This was a lengthy discussion, but some great ideas came out of it.

Modeling Unit 2

Unit II: Constant Velocity Particle Model
Using battery-powered buggies rolling across the table, we again worked through, What do you observe, What do can you measure, and what can you manipulate.  After going through this, we again developed our purpose (Chris led us to the procedure with Socratic dialogue) after starting with Jon's beginning statement (To determine the graphical and mathematical relationship between).  From there we were each given buggies (each a constant speed buggy, but each group's buggy traveled at a different speed), meter sticks and stopwatches (masking tape was also present if we wanted it).  The day drew to a close as most of the groups were finished plotting the data in  LoggerPro, and 3 groups shared their results on their whiteboards.

I'm guessing we'll finish our whiteboard discussion tomorrow.  One final think I'll add is that I've done a very similar lab at a 2 day physics workshop in Jacksonville.  However, the leader (another modeling guy with the exact same buggies) did it differently.  Each group was first given a blue buggy (all same, constant speed) and determine the relationship (found slope of d vs t graph).  When then had to turn that buggy in, and we were given a red buggy (again all red buggies were the same speed, all different speed than the blue buggies).  We again had to determine their speed.  At that point we had to turn in the red buggy as well.  The leader then asked us, using the mathematical models we had developed, to predict at what position the buggies would collide if a red stated at one end of the meter stick and the blue started at the other.  I'm not sure if we'll do that tomorrow, but I guess I'll found out then.

One other thing to point out, several of us asked if we should address plotting d vs t or t vs d with our students.  For the most part Jon and Chris were saying to make sure the students could justify why they were plotting it one or the other, and wait until later to broach that subject.  I'm not sure that we be as we progress through our whiteboard meeting or later in this cycle (or a future unit).

We started today by finishing our whiteboard discussion for our constant velocity lab (buggy lab).  As mentioned the previous post, Jon and Chris recommended to not worry about which variable was on a given axis (just make sure they had thought it through and had a reason).  However, they said as the whiteboard session is winding down, begin to force the discussion (with Socratic questions) to which graph ($d$ vs $t$ or $t$ vs $d$) gives more meaningful information (answer: $d$ vs $t$ since the slope is speed/velocity).  They also mentioned to direct the students to think about position and time interval rather than distance and elapsed time, as the former will help with the distinction of speed and velocity (which haven't been resolved as yet), and the concept of acceleration.

They also reminded us, that at this point in the year, the students "know" LoggerPro and scientific techniques learned in the first unit.  The supposedly know what slope means (but in reality they know how to calculate it, not what it means).

One important line of questioning to pose to the students is, "What does the slope of the $x$ vs $t$ graph represent?"

Slope is defined in algebra classes as the change in $y$ divided by the change in $x$.
$\large m= \frac{\Delta y}{\Delta x}$
Since the $y$-axis of a $x$ vs $t$ graph represents position, a change in position relative to a change in time, the slope represents the average speed over the elapsed time
$\large \overline{v}= \frac{\Delta x}{\Delta t}$
Since $\Delta x$ is a distance, it would have units $\textit m$.  $\Delta t$ is an elapsed time, so it would have units $\textit s$. Thus the slope of the x vs t graph should have units $\textit m/s$, which is consistent with the units for speed.  {Thanks Global Physics Department for introducing me to LaTex!}

Next on the agenda was using LoggerPro to create a $v$ vs $t$ graph for our data.  After which, we used the integral function to find the area under the "curve."  Again, we discussed the meaning of this area.  From math, we know:
$area=(base)(height)$
Since the base is time, $t$, and the height is velocity/speed, $v$, we can show that the area is displacement/distance.  In looking at my notes, one thing that I'll get clarification on, is when due we, the teacher, distinguish between speed/velocity and distance/displacement during this process.  Have we gotten to that point, and I forgot to note it, or are we not to that stage in the cycle.

Next on the agenda, we were asked to work on Unit II worksheets One & Two.  Each group was again  asked to present one part of this assignment on a whiteboard.  A few comments to note:
1. Jon mention that before beginning these experiments, he has the lab groups perform a vernier experiment using motion detectors and labquest mini interfaces to match their motion to given position vs time and velocity vs time graphs. (I mentioned that I do the same activity as a competition between lab groups, which I find gets the kids very excited.  I'll probably write about my "Physics Olympics" at some point in the near future.)
2. On wkst 1, question 2a, ask the group "How do you know they are the same?"  Meaning, get them to discover how the could determine the scales were the same given the limited information.
3. On wkst 1, question 2d, ask the group "Can two of your members enact the motion depicted in the graph?"
4. On wkst 2, question 6&7, use Socratic questioning to lead students to drawing dashed vertical lines at the points of discontinuity.  Someone asked about including open and closed dots to show where the object was at the point of discontinuity.  Chris answered that we don't know, nor do you need to get into that level of sophistication.
We ended the day by discussing the last tool in the modeling arsenal, Motion Maps:

The above examples show two different maps (the first above the red line, the second is below).  Some key features of the map are: the position vector, which shows the origin (X) and the direction of positive motion; the dot (which I couldn't get to work as a small dot); the arrow on the dot, which represents the velocity of the object at that location and time.

That's where we ended today.

We began today with work on worksheets four and five from Unit II.  While we were working on this, we got clarification of when to distinguish between vectors and scalars.  Jon said that you build it in slowly this unit and the next.  One trick that Jon recommended was to tell the students that scalar terms are shorter than their corresponding vector terms (speed/velocity, distance/displacement).  Remember, more letters in the word, more information.  Obviously, this won't help deepen the understanding of the concept, but it may help jog the memory for a student.

We all agreed that worksheet 5 does a great job of helping clarify the relationship between motion maps and and the other tools for modeling.  One thing someone mentioned is that they might have the students make basic, qualitative equations to bring that aspect into the fold.  Jon, while agreeing, also cautioned that we need to remember that motion maps are pseudo-quantitative at best.  Don't get too bogged down in the limits of the constant velocity model (what happens to the speed at the last instant shown on the graph?).  Chris mentioned that we need to make sure that the motion map does correctly depict the motion shown.  He illustrated this poignantly when one group had 3 points for their motion map.  One while it was moving away from the origin at constant speed, one while it was at rest, and a third while it was moving at constant speed toward the origin.  While at first trying to model to us how to lead the group with Socratic questioning, he saw the group presenting wasn't getting what he was selling. However, he kept at it and led the group to realize that they needed more than one point for each segment of the graph to show that the velocity was constant in a given section.

They also pointed out that a good convention to use is to put each type/segment of motion on a "different line," meaning if the object changes from one constant speed to another (stopping would constitute a new constant speed), put the first dot for the new motion slightly above (or below) the first set of points.  They also clarified to work from the displacement vector away (i.e.: if drawing above said reference, each segment is place higher).

To finish up the unit, Jon and Chris again elicited feedback.  We said we liked worksheet 5 (converting between the different tools of modeling), having students enact the motion shown in motion maps or velocity-time graphs, and the motion mapping activity with the vernier motion sensors.

Modeling Unit 1

As I noted at the top of my "modeling" page, I'm going to go back and reorganize my blog posts.  I've found that organizing by the day of the workshop isn't very effective.  I plan to try to go back and organize the posts based on the Unit in the modeling cycle.  So, here's Unit 1 (with the preliminary stuff of the workshop added in):

I'm blogging about my experience at the FIU Modeling Workshop.  Much of this is for me, so that I can remember my experience.  However, maybe this will help someone else to come over to the Modeling Method.  I'm not sure if I've mentioned it before, so I might as well state it here, I currently teach Standard, Honors, and AP-B Physics.  I've been using the CPO Program, which is a hands-on program.  To me, it's biggest downfall is that the labs, although well constructed, are cookbook labs.  The students can get caught up in the procedure, and miss the concept.  After joining twitter, I've come across several teachers that use the Modeling Method, and have become more and more interested.  Which brings me back to the point of this post, my experience on the first day.  However, before I get into that, I would make the following claim, if this interests you, please go to the workshop, don't just rely on me.  Even after only one day I can tell that my recount will mean nothing for you without you attending.

Day 1:
We started the day with our leaders introducing themselves (Jon Anderson and Chris Doscher).  They quickly led us through a great introductory activity, that I might very well use with my students.  We each had to come up with 2 truths and 1 lie about our self, and the other people in our small group had to try to determine which is the lie.  After that, each person in the group had to introduce another member from the group to the entire cohort.  To me, it was a fun way to break the ice.

After taking the Force Concept Inventory test, we then got our first taste of whiteboarding.  We were asked to answer the following 3 questions as a group:
1. What are your greatest content-related teaching challenges?
2. What are your greatest instructional teaching challenges?
3. What are your goals for this workshop?

Here are the whiteboards:

Unit 1: Scientific Thinking
After breaking for lunch, we began our first experiment, a Pendulum Experiment.

In walking us through the experience of the lab, we were given a few questions and comments after we completed the task.  (For the sake of brevity, I'll omit our responses to the questions).

Jon set up a simple pendulum and then wrote the following questions in succession:

What do you observe?
(side note, Brian W. Frank  recommended asking "what do you notice," rather than "what do you observe." Here's why)
• Jon mentioned to try to not give any comments/facial gestures, just write.
• Ask if you need to rephrase for fewer words
What can you measure?
• Don’t comment until at the end.
• Do you need to pare down the list, do to lack of equipment?
• Are any measurements redundant, if so discuss with the class.
What can you manipulate to change the time?
• Edit down after complete based on equipment present
State purpose of lab for students:
To determine the mathematical and graphical relationships that exist between time, length, mass, and angle of release of a simple pendulum.
(Jon told us that the bold part represents the beginning phrase for basically all the lab objectives)

Before assigning the different types of relationships to different groups, Jon told us two important "rules" for labs:
1. Fair Test: manipulate only one variable at a time
2. 8x10 rule: collect at least 8 data points separated by at least a factor of 10
After collecting the data, they then introduced the group to LoggerPro, to analyze the data. We used LoggerPro to analyze our results and then put them on whiteboards to share with the other groups.

During this time, my small group discussed some of the strength and weaknesses with excel vs LoggerPro.  Namely, to us LoggerPro can analyze the data faster, but excel integrates with word docs a little easier.  (We could easily be wrong on this.)

Well, that's basically it.  A good first day, and I'm excited for the second day.

To start of today, we finished up the "Board Meeting" with the groups that studied length vs period.  For physics teachers, this is obviously the group that was able to show an actual correlation.  One of the most interesting parts of the discussion, to me, was when Jon and Chris recommended not worrying about linearization yet.  They told us to now worry about that battle, as it will come up as you move into the next phase of the cycle.  Just let the kids use LoggerPro to get the mathematical relationship.  They did recommend spending some time to discuss whether or not the data should go through the origin.  In the course of that discussion then mentioned what they called the "5% Rule" which basically states that if the y-intercept is less than 5% of the biggest measured value in the data for the y axis, assume that it goes through the origin.

After we finished that discussion, we then moved into the next phase of the modeling cycle in which we worked on linearizing data using LoggerPro.  The worksheet had 6 data sets (we had version 3 of this worksheet, I'll add that link if I find it), and we had to plot the data and determine how to manipulate the data to create a linear graph that went through the origin.  Jon and Chris mention that they only used the first four problems (which I think are the 4 in version 2) with their classes as they have found that they are sufficient to get the students acclimated to the process. Jon and Chris did recommend to have the students write the regressed equation rather than the proportion shown (ie: equation with slope and y-intercept, not y is proportional to 1/x).

After we had linearized the data, each group was assigned a different problem to put on a whiteboard to share with the cohort.  Again, we were able to get a greater feel for how the whiteboarding process works, and able to ask questions as to how to moderate, when to step in and when to let the conversation go.

After that, Jon and Chris asked for feedback as to how we thought the first unit went.  It's amazing how well these modeling people all act as I remember Frank Noschese blogging about getting feedback from students more often than just the end of the year (read the post here).

They asked what worked and what didn't?  To the first we said, we liked learning: how to use LoggerPro (especially for linearization), the linearization summary sheet, breaking up the pendulum lab to finish the lab in less time (made groups take more ownership of work since others were depending on them to get it right), and using inductive reasoning to determine relationship instead of the teacher just telling "us" the answer.  What we didn't like: some wanted more explicit explanation of the relationships between independent and dependent variables (hopefully I'm remembering that correctly), and some wanted the workshop to move a little faster (I think she was referring to limiting some of the discussion, but Chris rephrased it as getting started quicker/more punctual coming out of breaks.  I'm not sure which was what she meant).

Thursday, September 15, 2011

Buggy Lab

Throughout the day, I've seen and been a part of a great discussion about how to do the Modeling Buggy Lab.  For those not familiar, think classic algebra problem with 2 trains.  After screaming, "I hated that problem!" Ask yourself what did you dislike about it?  Probably the fact that it had no context.  This is where modeling steps in.

Here's the set up, you show the class a motorized car that moves at constant speed.  And, through socratic questioning, lead them to realize that the position and elapsed time are related.  You then ask them to determine the "graphical and mathematical" relationship between position and elapsed time (or clock reading).  You leave it up to the students to figure out how to find those relationships.

If you try this, your students might come up with one of these two solutions, (A) set up fixed distances and measure the time to travel those distances, or (B) place marks at distances for fixed values of time (place a piece of tape where the car is at 1 sec, 2 sec, ...)

This is where are tweebate begins.  Since the "convention" is to plot the independent variable on the horizontal axis, the two different means of collecting data would produce two different plots.  Option A, since the student set up fixed distances, that would be the independent variable.  Thus elapsed time (clock reading) would be on the vertical axis and distance traveled (or more specifically position) on the horizontal.  Option B would yield the opposite.

Our debate was whether or not we should let this happen.  Also discussed was the above was ok, but to just tell them to all plot time on the horizontal axis.

So here's my two cents:
What I love about the modeling curriculum is that we (teachers) are trying to foster discussion, which in the end should induce critical thinking skills.  So to me, let the students measure it how they think they should.  Let them graph it how they think they should.  As they all come together in the "Board Meeting," where they share their results, as the teacher try to help them draw out the important conclusion.  Did the two methods produce different results?  Did both methods produce a straight line?  What does that say about the relationship between position and time for the buggy?  Assuming the buggies go at the same speed, how do the slopes compare? If some have a slope that has units of m/s and some have s/m, lead them to generate the algebraic equation for the line.  Have one group rearrange their equation
$y=mx+b$

$\large x=\frac{y-b}{m}$

Discussing the "10% rule" which helps them figure out if the y-intercept is significant, can also come into play here.  If $b$ is 0, then:
$\large x=\left(\frac{1}{m}\right)y$

Thus, how do the slopes compare.  Again if the cars all travel at the same approximate speed, won't this be a great aha moment?  To me it's worth the time, rather than the teacher merely saying, "Don't worry about the convention you learned in middle school, just plot it this way."  In no way am I trying to demean those that do this, I just think it's worth the 10 minutes to let the discussion play out.

If you have the time, you can also bring in the discussion of slope recommended by Arons, the "bible" of physics teachers (personally, I think it's an amazing book, but it's still no Bible, sorry Arons).  He recommends discussing the meaning of slope.  What does the slope of position vs time mean?  Most students will probably respond "change in y over change in x," which would confirm what Arons suggests. He writes that most students don't understand slope, they just know how to calculate it.  This is where you can take another 10 minutes and lead the students to realize that option A will produce a graph the measures how fast the buggy is moving while group B will produce a graph that measures how slow it is moving.  This is now a great time to lead them to see why the convention of independent variables on the horizontal and dependent on the vertical is not a convention that is always used.  Rather think ahead of the relationship you want to show, then set up the axes to show that relationship.
I know I'm new at this, so I would love to hear where, other than possibly time, we wouldn't want to have these discussions.

PS - for those wondering where the train problem comes in - take away the first buggy and now give them a second buggy (which travels at a different constant speed).  While the students turn in that buggy, have them graph (and find equation for the slope) the data for the second buggy.  Now, without the buggies in hand, have them predict where the collision will occur if you start them at opposite ends (meter stick, room, table, etc).  Viola, the train problem will come to life.  I did this with my AP kids and they were so excited when they say that their calculation was "right"  (read within error predicted by a monte carlo analysis, which I say a big thank you to Andy and the rest of the crew in the Global Physics Dept).